Stock futures pricing based on the minimal martingale measure in discrete-time incomplete markets

The increasing interest in financial innovation of enterprises has heightened the need for the knowledge of accurate pricing for derivatives in actual discrete-time incomplete market, especially for futures, the most actively traded derivatives in China. Nevertheless, even contingent claim pricing in such markets have few previous researches concentrated on, quite apart from futures. This paper develops stock futures pricing in discrete-time incomplete markets based on the minimal martingale measure and the locally risk-minimizing strategy. The author establishes a specified market model, in which the minimal martingale measure is worked out. Under the measure the arbitrage-free pricing model for stock futures is obtained. By using data of several representative stock futures and stock index futures selected from American financial markets, an empirical test is implemented to investigate the efficiency of the model. The results indicate that the predicting prices given by the new model could fit the actual prices well, and compared to a traditional single-factor model, the new model is strongly possible to perform better in prediction. These results offer attractive possibilities for applications.